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Converse of CPCTC Demonstration

Converse of CPCTC Demonstration
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2016-06-14 08:46
TriangleAngleGeometric Construction
In collections Triangle Congruence Criteria Exploration
This example illustrates the application of the converse of CPCTC (Corresponding Parts of Congruent Triangles are Congruent), showing that if two triangles have equal corresponding sides and angles, they are congruent. It involves core concepts like triangle congruence criteria, corresponding side-angle relationships, and geometric construction. The construction uses commands/objects such as Polygon, Line, Angle, Mirror, Rotate, and Midpoint in GeoGebra to build and verify congruence conditions. Suitable for high school mathematics instruction to visually understand the application of congruence criteria and their converses.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → Triangle1, c, a, b
  2. Line(F, I) → f
  3. Angle(B, A, C) → α
  4. Angle(A, C, B) → β
  5. Angle(C, B, A) → γ
  6. Mirror(A, f) → A'
  7. Mirror(B, f) → B'
  8. Mirror(C, f) → C'
  9. Polygon(A', B', C') → Triangle2, c', a', b'
  10. Angle(B', C', A') → δ
  11. Angle(C', A', B') → ε
  12. Angle(A', B', C') → ζ
  13. Rotate(A, (-(45°)), F) → A'_1
  14. Rotate(B, (-(45°)), F) → B'_1
  15. Rotate(C, (-(45°)), F) → C'_1
  16. Polygon(A'_1, B'_1, C'_1) → Triangle3, c'_1, a'_1, b'_1
  17. Angle(B'_1, A'_1, C'_1) → η
  18. Angle(A'_1, C'_1, B'_1) → θ
  19. Angle(C'_1, B'_1, A'_1) → ι
  20. Midpoint(b) → D
  21. Rotate(A, 180°, D) → A'_2
  22. Rotate(B, 180°, D) → B'_2
  23. Rotate(C, 180°, D) → C'_2
  24. Polygon(A'_2, B'_2, C'_2) → Triangle4, c'_2, a'_2, b'_2
  25. Angle(C'_2, B'_2, A'_2) → κ
  26. Angle(c'_2, b) → λ
  27. Angle(A'_2, C'_2, B'_2) → μ